Do any records survive of the census mentioned in Luke?
Well a quick google search pulled up a couple of neat sites
csun.edu/~hcfll004/romancensus.html was neat but didn’t cite it’s original source.
I’ve looked for information about the census before and I think Origen and Justin Martyr mentioned census records in Rome recording Jesus but I can’t find them now, or perhaps it was Tertullian and Ireaneus. I thought New Advent’s site had some details about it but I can’t find the page right now.
The census mentioned in Luke’s Gospel posses some difficulties. Both Matthew and Luke put Jesus’ birth during the reign of Herod the Great who died in 4 BC. However the first Roman census including Judea was the Census of Quirinius, which was conducted around AD 6.
Here’s some interesting information:
On Herod the Great